I would cut a rectangular section out of the front faceplate right where the smart card reader slot is. make it just big enough to hold the LCD unit (not the PC board, but the display unit on the board).
Then, get a piece of lightly smoked plexiglass, cut it about 1cm larger than the hole and lightly bevel the edges so it looks nice. on another project I used 400-600 grit sandpaper on a vibrating hand sander and lightly worked the edges of the plexiglass. On my last project, I sanded the edges square and gave the front surface a *slight* bevel. this gives it a nice, finished look. Be careful not to scratch the front surface!
once it's finished, align and glue it over the LCD cutoutt with clear epoxy (use very little so it doesn't squeeze out the sides)
Results should look pretty good, and you can save the CD rom bay for something useful.